# Study on Share Rate of Support Structure for Super-Large Span Twin Tunnels with Small Interval

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Daling Tunnel

#### 2.2. Theoretical Load

#### 2.3. Finite-Element Model

^{2}downward and applied to all elements. The model is shown in Figure 4; (Since the models of the primary support and secondary lining are similar, only one model is shown as an example.)

#### 2.4. Field Measurement

- (1)
- Settlement of the vault of primary support was measured by total stations and steel rulers to find out the share rate of primary support.
- (2)
- Stress of the secondary lining (derived from the strain) was measured by concrete strain gauges. The gauges were put on both sides of the secondary lining at each point. This is for finding out the share rate of secondary lining. The arrangement of concrete strains is shown in Figure 6.
- (3)
- Total pressure of the primary support and secondary lining was measured by pressure cells arranged at the points A, B, and C at the outside of the primary support. This is for comparison and verification. The arrangement of pressure cells is shown in Figure 7.

## 3. Theoretical Calculation of Surrounding Rock Pressure

#### 3.1. Failure Mode and Assumptions

_{1}, W

_{2}, and W

_{3}are the gravity of the rock mass A’C’E’ (ACE), IKOM, and I’KOM’, respectively. T

_{1}and T

_{2}are the frictional force caused by the soil on both sides of the tunnel to resist the settlement of the vault. Furthermore, ${\phi}_{c}$ is the simplified internal friction angle of the surrounding rock. According to the Chinese standard, ${\phi}_{c}$ is usually greater than the real internal friction angle ($\phi $). When using ${\phi}_{c}$, it is valid regardless of the cohesion force). $\theta $ is determined by referring to the Chinese standard. Here are some explanation and hypotheses for this sliding failure mode:

- (1)
- Suppose that the ground was horizontal, the rock mass was homogenous, and isotropic and the twin tunnel was symmetry and parallel. Moreover, excavation of left and right holes is sequent and full section.
- (2)
- The excavation of the first hole is similar to an ordinary single-hole tunnel. It means that the fracture planes on both sides of the first hole, which are shown as A’C’ and M’J’ in Figure 8, are two inclined straight planes, and at an angle of ${\beta}_{1}$ to the horizon. In addition, the pressure inside and outside (shown in Figure 8) is symmetric.
- (3)
- When the following hole is excavated, the fracture plane at the outside of the hole (AC) is at angle ${\beta}_{1}$ to the horizon, while at the inside of the hole the angle of the fracture plane (MO) is assumed as ${\beta}_{2}$. Focus on the triangle OJJ’, when the following hole is excavated, it is inclined to slide down along the plane JM. However, since the excavation of the first hole has induced a relative slippage at the plane OJ’ and undermines the cohesion force along the plane OJ’, usually the triangle OJJ’ will not slide and fracture along the plane JO. Instead, the tensile fracture plane will be formed in the triangle OJJ’, which is assumed as a vertical plane (OK). In summary, the fracture plane at the inside of the following hole is assumed as KOM.
- (4)
- According to the sliding trend of the triangle OJJ’ caused by the sequent excavation of the twin tunnel, and based on the theory of soil mechanics, the interactive force (N) in normal direction at the fracture plane OK must be less than the earth pressure at-rest. For safety, let N equal 0.

#### 3.2. Calculation of Theoretical Load

**(1) Surrounding rock pressure of the first hole**

**(2) Surrounding rock pressure of the following hole**

_{2}′ can be solved as:

## 4. Results and Discussion

#### 4.1. Share Rate of the Primary Support

#### 4.2. Share Rate of the Secondary Lining

^{2}) is the area of the cross section, I (m

^{4}) is the moment of inertia of the section, y (m) is the distance between the neutral axis, and the edge, ${\sigma}_{\mathrm{inside}}$ (MPa) is the stress of the concrete at the side of the inner section and ${\sigma}_{\mathrm{outside}}$ (MPa) is the stress of the concrete at the side of surrounding rock.

#### 4.3. Total Pressure for Verification

#### 4.4. Discussion

- (1)
- The influence of the construction’s sequence of the first hole and following hole was not considered in this research, and the way of excavation was assumed as full section excavation.
- (2)
- This paper supposed that the stratum was consistent and the surrounding rock mass was ideal.
- (3)
- The surface of earth was presumed to be horizontal, and so on.

## 5. Conclusions

- (1)
- The formulas of calculating surrounding rock pressure of normal tunnels (usually including two or three lanes) in Chinese standard could be applied to the super-large span twin tunnels (including four or more lanes). The method was verified by field measurement.
- (2)
- The method of researching the share rate of the primary support and the secondary lining of the tunnel was proposed. The result demonstrates that the share rate of the primary support and the secondary lining of Daling Tunnel are both 40%. Usually for twin tunnels with super-large span in cities, not only the primary support but also the secondary lining should be strong enough to ensure the design is safe and reliable. In addition, this conclusion is conservative when compared to the measurement, which is practical for application in engineering.
- (3)
- The result of the theoretical calculation and numerical simulation was compared with the measurement to evaluate the research methodology and achievements. These two results match properly, which verify the correctness of this study. Hence the conclusions and the method of this research can make some reference to the design, construction, and maintenance of super-large span twin tunnels.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**The process of this research. Numerical simulation and field measurement are combined to find out the share rates of primary support and secondary lining. Verification is proposed in final phase.

**Figure 2.**Information of Daling Tunnel. For optimal traffic capacity, these twin tunnels have super-large span and small interval. The main body of them are both composite lining and bolts.

**Figure 3.**Theoretical load of Daling Tunnel (unit: kPa). The process of calculation will be mentioned in Section 3.

**Figure 4.**The finite-element model of simulation. It is a load-structure model and mainly simulated by beam elements and springs.

**Figure 6.**Concrete strain gauges in secondary lining. The most internal force of secondary lining can be obtained by the gauges.

**Figure 7.**Pressure cells between surrounding rock and primary support. By these cells, the total pressure of the primary support and secondary lining can be measured.

**Figure 10.**Measured and simulated vault settlement. When primary support is under 40% of the theoretical load, the result of simulation is in accord with the measurement.

**Figure 12.**Measured concrete stress of the secondary lining. It went stable after about a month. (

**a**) inside secondary lining; (

**b**) outside secondary lining.

**Figure 13.**Safety factors of simulation and measurement. The deviation is about 25% averagely and mainly attributed to the efficiency of the rebar in secondary lining.

**Figure 14.**Total pressure of the primary support and the secondary lining. There is about 20% deviation at each point and it is believed to be born mainly by advance support and the surrounding rock itself.

Parameter | Value |
---|---|

Unit weight, $\gamma $ (kN/m^{3}) | 20 |

Simplified internal friction angle, ${\phi}_{c}$ | 45° |

Real internal friction angle, $\phi $ | 22° |

Friction angle of the sliding plane, $\theta $ | 13.2° ($0.6\times \phi $) |

Span, B (m) | 19.4 |

Height, H_{l} (m) | 12.9 |

Net interval, D (m) | 12.6 |

Buried depth, H (m) | 20 |

Part | Young’s Model /GPa | Poisson’s Ratio | Unit Weight /kN/m ^{3} | Thickness /m |
---|---|---|---|---|

Primary Support | 25.3 | 0.2 | 25 | 0.3 |

Secondary Lining | 28 | 0.2 | 25 | 0.7 |

Item | Position | Axis Force /kN | Moment /kN·m | Eccentricity /mm | Attribute | Safety Factor |
---|---|---|---|---|---|---|

Simulation | Vault | −1080 | −222 | 493 | All is small eccentricity | 9.47 |

Left haunch | −1432 | 204 | 430 | 8.19 | ||

Left sidewall | −1572 | −32.6 | 308 | 10.41 | ||

Right haunch | −1432 | 204 | 430 | 8.19 | ||

Right sidewall | −1572 | −32.6 | 308 | 10.41 | ||

Measurement | Vault | −1723 | −53 | 318 | 7.85 | |

Left haunch | −1216 | 24 | 307 | 11.54 | ||

Left sidewall | −781 | 71 | 378 | 14.0 | ||

Right haunch | −1348 | −36 | 314 | 10.17 | ||

Right sidewall | −862 | 38 | 332 | 15.00 |

Measured Point | Theoretical Load /kPa | 80% of the Theoretical Load /kPa | Measured Pressure /kPa | Deviation /% |
---|---|---|---|---|

A | 286.90 | 229.56 | 180.94 | 21.18 |

B | 211.63 | 169.30 | 142.68 | 15.73 |

C | 98.40 | 78.72 | 65.36 | 16.97 |

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## Share and Cite

**MDPI and ACS Style**

Zhao, X.; Sun, K.; Zhen, Y.; Hong, Y.; Zhou, H.
Study on Share Rate of Support Structure for Super-Large Span Twin Tunnels with Small Interval. *Appl. Sci.* **2022**, *12*, 7498.
https://doi.org/10.3390/app12157498

**AMA Style**

Zhao X, Sun K, Zhen Y, Hong Y, Zhou H.
Study on Share Rate of Support Structure for Super-Large Span Twin Tunnels with Small Interval. *Applied Sciences*. 2022; 12(15):7498.
https://doi.org/10.3390/app12157498

**Chicago/Turabian Style**

Zhao, Xuwei, Keguo Sun, Yingzhou Zhen, Yiqin Hong, and Huichao Zhou.
2022. "Study on Share Rate of Support Structure for Super-Large Span Twin Tunnels with Small Interval" *Applied Sciences* 12, no. 15: 7498.
https://doi.org/10.3390/app12157498